Stochastic Gain Research Articles

Robust Properties of Risk-Sensitive Control

It is well-known that there are strong connections between risk-sensitive stochastic control and deterministic H/sub /spl infin// control. These connections have stimulated interest in the risk-sensitive control problem. But is the risk-sensitive controller robust? This paper answers this question in an affirmative and precise way, and gives a stochastic small gain theorem and a stochastic robust stability result.

Stochastic Acceleration and Nonthermal Radiation in Clusters of Galaxies.

We calculate the distribution of electrons in clusters of galaxies, which results from thermalization processes in the presence of stochastic acceleration due to plasma waves. We show that the electron distribution can deviate from a Maxwell-Boltzmann distribution because of the effect of the stochastic energy gain, provided that waves can be sustained against damping. The bremsstrahlung emission of the nonthermal tail of electrons can result in a flux of hard X-rays that is compatible with the ones recently detected in some clusters of galaxies.

Longitudinal Landing Control Law for an Autonomous Reentry Vehicle

This paper discusses the longitudinal ight-pathcontrol lawdesigned and  ight tested for theAutomaticLanding Flight Experiment (ALFLEX). ALFLEX, for which  ight tests were conducted in 1996, demonstrated Japanese potential for developing automatic landing technology for a reentry space vehicle. One of the critical factors in satisfying the design requirements for landing on a limited length runway was longitudinal  ight-path control following the pre are maneuver. Robustness against uncertainties and sensor errors is a key issue in longitudinal  ight-path control. The longitudinalguidance and control lawswere carefully designed and  ight tested. Although the  ight tests proved that the design satisŽ ed all landing requirements, it identiŽ ed critical parameters affecting landing performance such as vehicle longitudinal aerodynamics, navigation error, and air data sensor error. This paper describes data obtained during the development and  ight tests, as well as further investigations conducted after the  ight tests in order to improve landing performance for future space vehicle developments. In the subsequent design review a new approach called stochastic gain tuning was adopted, where the guidance feedback gain is tuned to maximize the probability of mission success. The results indicate some possibility of improvement of robustness.

Stochastic matched field processing

Stochastic matched field processing was introduced [Baggeroer and Kuperman, J. Acoust. Soc. Am. 91] as a means to address stochastic variability and signal gain degradation in a replica signal. The approach parallels what is usually termed the ‘‘random signal in noise’’ problem in time series analysis wherein one uses a stochastic model to respond to the signal gain degradation issue when high-fidelity replicas cannot be generated. For stochastic MFP the important issues are: (i) the signal power scatters into a ‘‘red’’ spectra of eigenvalues where only a small number are significant, (ii) the eigenvectors are predictable based upon a priori environmental data such as internal wave or signal motion models in addition to nominal sound speed models. For many environments these conditions are met and, and importantly, more robust, MFP can be obtained. This presentation will review (i) stochastic matched field, (ii) apply it to deep and shallow water random ocean models, and (iii) assess its performance using Chernoff detection theory bounds for low signal-to-noise ratio scenarios.

The influence of stochastic nonlinear gain variation on bright soliton transmission system

The model of stochastic nonlinear gain variation is built in the soliton transmission system. The influence of the stochastic nonlinear gain variation on the soliton transmission system is studied. The results show that the stochastic nonlinear gain variation apparently leads to the time jitters in arrival, degrades the capacity of soliton transmission system and the filter can suppress the influence well.

Stochastic retinal mechanisms of light adaptation and gain control.

Under appropriate experimental conditions, the threshold intensity of a visual stimulus varies as the square-root of the background illuminance. This square-root law has been observed in both psychophysical threshold experiments and in measurements of the thresholds of individual ganglion cells. A signal detection theory developed in the 1940s by H. L. de Vries and A. Rose, and since elaborated by H. B. Barlow and others, explains the square-root law on the basis of 'noise' due to fluctuations in the number of photon absorptions per unit area and unit time at the cornea. An alternative account of the square-root law--and also other threshold-vs-intensity slopes--is founded on the assumption of physiological gain control (W. A. H. Rushton, Proc, Roy. Soc. (London) B 162, 20-46, 1965; W. S. Geisler, J. Physiol. (London) 312, 165-179, 1979). In this paper, a neural model of light adaptation and gain control is described that shows how these two accounts of the square-root law can be reconciled by a stochastic gain control mechanism whose gain depends on the photon fluctuation level. The process by which spikes are generated in a ganglion cell is modeled in terms of a stochastic integrate-and-fire mechanism; this model is used to quantitatively fit toad retinal ganglion cell threshold data. A psychophysical model is then outlined showing how a statistical observer could analyze the ganglion cell spike trains generated by 'signal' and 'noise' trials in order to statistically discriminate the two conditions. The model is also shown to account for some dynamic aspects of ganglion cell responses, including ON- and OFF-responses. The neural light adaptation model predicts that--under the proper conditions--brightness matching judgments will also be subject to a square-root law. Experimental tests of the model under superthreshold conditions are proposed.

Stochastic gain in the cyclotron resonance laser accelerators

A Hamiltonian description modelling the interaction of electrons with laser beams traversing the static magnetic field is presented. It is found that the absolute energy gain of the particle is a sensitive function of the entry phase, initial velocity, and the amplitude of the electromagnetic wave. Graphical representation of the numerical simulation shows the emergence of fractal patterns throughout the phase space.

Iterative reduction of gain variations in parallel electron energy loss spectrometry

We discuss a method of reducing intrinsic gain variations of the detector array in parallel electron energy loss spectrometry (PEELS). Two or more spectra are acquired independently, but under the same experimental conditions, except that the spectra are shifted over the array with respect to each other by a certain amount. For stochastic gain variations the problem is solved in closed form. It is shown that the reduction of the variance of gain variations increases with the squareroot of number of iterations. Simulations for a purely stochastic gain spectrum prove the predictions. Experimental gain spectra turn out to be non-random. The consequence of non-stochasticity (correlations between channels in the array) can be understood within the theory. The proposed method is useful for any experiment involving a linear or two-dimensional detector array where it is not possible to obtain a “flat field” spectrum.

Statistics of laser intensity after passing through an amplifier with stochastic gain distributions

Statistical moments of laser intensity passing through an amplifier with stochastic gain are evaluated. This situation happens when turbulent flows exist in the gain medium, which is assumed to be a two-level atomic system. Also, it is assumed that the turbulence structure is fully characterized by a stochastic process. This gain medium is assumed to be partially homogeneously broadened and slightly saturated. In the derivations, the paraxial approximation is combined with the perturbation method to solve for the random laser field inside the amplifier. For mathematical simplicity, a plane wave is propagated through the gain medium which contains only weak turbulence fluctuations. Dependences of the average laser intensity and contrast on turbulence fluctuation strength, characteristic length of the turbulence, and gain saturation and numerically demonstrated. It is found that the turbulence fluctuations make both average intensity and contrast stronger. Also, the gain saturation reduces both average intensity and contrast. In addition, it is shown that the contrast increases as the characteristic length of turbulence is increased.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Average intensity and contrast of light amplified by a partially homogeneously broadened, slightly saturated laser amplifier with stochastic gain distributions

We evaluate the average intensity and contrast of the output of a laser amplifier in which stochastic gain distributions exist. This situation occurs when turbulence flows are developed in a gas- or liquid-laser amplifier. The gain medium is assumed to be partially homogeneously broadened and slightly saturated and to consist of two-level atoms. In our computations, a plane wave is propagated through the gain medium with weak turbulences, under the assumption that the size of the first Fresnel zone is much smaller than the characteristic length of turbulences.

Frequency domain stability criteria for stochastic systems

The stability of a class of dynamical systems containing random parameters is investigated. An input-output stability concept is formulated for stochastic systems. The specific class of systems considered consists of those feedback systems whose open loop consists of the cascade of a white noise multiplicative gain and a linear deterministic dynamical system. Necessary and sufficient frequency domain conditions for stability are derived and it is shown that the uncertainty has a destabilizing effect. The resulting stability conditions depend on the open-loop stability, the rms value of the stochastic gain element, and the effective bandwidth of the linear element.